Pith. sign in

REVIEW 2 major objections 5 minor 2 cited by

Improved structure of calcium isotopes from ab initio calculations

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Including three-body operators in IMSRG calculations lowers the predicted $^{48}$Ca first $2^+$ excitation energy by about 0.68 MeV, bringing it close to experiment and strengthening the description of the $N=28$ shell closure.

desk verdict A careful, transparent IMSRG(3)-N7 study of calcium isotopes with a genuine but not yet converged correction to the 48Ca 2+ energy, and a robust negative result on the charge-radius puzzle. read the letter →

arxiv 2411.16014 v2 pith:J3QVIUIZ submitted 2024-11-24 nucl-th

M. Heinz , T. Miyagi , S. R. Stroberg , A. Tichai , K. Hebeler , A. Schwenk This is my paper · ORCID
classification nucl-th PACS 21.60.Cs27.40.+z21.10.Ft
keywords calciumisotopesin-mediumsimilarityrenormalizationgroupthree-bodyoperatorschargeradii2+excitationenergyshellclosureN=28many-bodyuncertaintyabinitionuclearstructure
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tests whether a known weakness of the in-medium similarity renormalization group (IMSRG) at two-body truncation, the overprediction of the first $2^+$ excitation energy of $^{48}$Ca, is cured by including three-body operators in the flow. In the IMSRG(3)-$N^7$ calculation the $2^+$ energy drops by about 0.68 MeV at the largest three-body model space used, moving from 4.930 MeV toward the measured 3.832 MeV and toward coupled-cluster results with triples. The authors then ask whether the same upgrade fixes the underpredicted charge radius of $^{52}$Ca relative to $^{48}$Ca, and find that it does not: the corrections are nearly identical in the two isotopes and largely cancel in the difference. The same calculations provide size-extensivity-based estimates that IMSRG(2) carries roughly 2-3% uncertainty on correlation energies, 1-1.5% on charge radii, and 5-7.5% on neutron skins.

What carries the argument

The central object is the IMSRG(3)-$N^7$: an in-medium similarity renormalization group evolution that includes normal-ordered three-body operators $W(s)$ throughout the flow, truncated to all terms that scale no worse than $N^7$ in basis size. After decoupling the $^{40}$Ca core and the $0\hbar\omega$ neutron valence space, the residual three-body valence-space operators are set to zero following the cluster hierarchy (one-body effects dominate two-body, which dominate three-body), and a standard shell-model diagonalization is performed. The mechanism carrying the argument is that induced three-body operators feed back into the effective one- and two-body valence-space interactions, lowering the computed excitation spectrum; because the IMSRG is size extensive, meaning errors scale with the system rather than growing disproportionately, the observed correction sizes can be quoted as transferable uncertainty estimates for IMSRG(2) in other medium-mass systems.

What would settle it

Recompute the $^{48}$Ca first $2^+$ energy retaining the three-body valence-space operators in the final diagonalization, or with $e_{\max,3b}>6$ (e.g., $e_{\max,3b}=7$) on a tractable model space; if the converged value moves back above roughly 4.5 MeV, the claimed improvement would be a truncation artifact rather than a many-body correction.

Watch

Extended reading notes

Core claim

The paper's central finding is that the valence-space IMSRG(3)-$N^7$, which keeps normal-ordered three-body operators while solving the renormalization-group flow and then omits them in the final shell-model diagonalization, changes calcium spectra substantially while leaving isotope shifts of charge radii almost untouched. For $^{48}$Ca the first $2^+$ state falls from 4.930 MeV in VS-IMSRG(2) by $-0.68$ MeV at $e_{\max,3b}=6$, $E_{3\max}=18$, reducing the gap to experiment from about 1.1 MeV to about 0.42 MeV and matching the direction and size of triple-excitation corrections in coupled-cluster theory. All predicted levels in $^{44}$Ca, $^{48}$Ca, and $^{52}$Ca are shifted downward by a roughly common factor that is largest for $^{48}$Ca. For charge radii, the IMSRG(3)-$N^7$ corrections to $^{44}$Ca, $^{48}$Ca, and $^{52}$Ca are strongly correlated, so the differences $R_{\rm ch}(^{52}{\rm Ca})-R_{\rm ch}(^{48}{\rm Ca})$ and $R_{\rm ch}(^{44}{\rm Ca})-R_{\rm ch}(^{48}{\rm Ca})$ barely move and the large measured $^{52}$Ca-$^{48}$Ca radius difference remains underpredicted. The paper reads these results as showing that the $2^+$ discrepancy was largely a many-body truncation artifact, while the radius puzzle is not resolved at this order.

Load-bearing premise

The headline correction assumes that the three-body model-space truncation ($e_{\max,3b}\le 6$, $E_{3\max}\le 18$) and the dropping of three-body valence-space operators before diagonalization are sufficient to fix the sign and size of the $2^+$ shift, even though that shift is not fully converged.

Editorial extensions

If this is right

  • VS-IMSRG(2) $2^+$ energies in closed-shell nuclei such as $^{48}$Ca can be off by roughly 0.7 MeV from the higher-order result, so comparing such states to experiment requires the three-body truncation or a comparable uncertainty estimate.
  • The $^{48}$Ca $2^+$ value is not fully converged at $e_{\max,3b}=6$, $E_{3\max}=18$, so the final prediction will move somewhat as the three-body model space grows, but the correction has a definite sign and approximate size.
  • Charge-radius isotope shifts in the calcium chain change by less than 10% when going from IMSRG(2) to IMSRG(3)-$N^7$, so the underprediction of the $^{52}$Ca-$^{48}$Ca difference is not a many-body truncation effect at this order.
  • For soft chiral Hamiltonians, IMSRG(2) results should be assigned uncertainties of roughly 2-3% on correlation energies, 1-1.5% on charge radii, and 5-7.5% on neutron skins.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension: apply the same VS-IMSRG(3)-$N^7$ treatment to other closed-shell nuclei with overpredicted $2^+$ states, such as $^{78}$Ni, to see whether the calcium-sized downward shift generalizes.
  • Because the radius corrections cancel almost completely in isotope differences, the persistent $^{52}$Ca-$^{48}$Ca puzzle likely sits in the Hamiltonian or in physics outside this truncation, such as multishell valence-space excitations, rather than in the IMSRG(2) approximation.
  • One could directly test the cluster-hierarchy assumption by keeping the three-body valence-space operators in the final diagonalization with a three-body-capable shell-model solver; the paper predicts their effect is small, so a noticeable shift would mark a boundary of the approximation.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper applies the recently developed IMSRG(3)-N7 and VS-IMSRG(3)-N7 methods to the calcium isotopes 44Ca, 48Ca, and 52Ca using the 1.8/2.0 (EM) chiral Hamiltonian. It reports that the VS-IMSRG(3)-N7 corrections to the first 2+ excitation energy of 48Ca are large and bring the prediction closer to experiment and to coupled-cluster results with triples, improving the description of the N=28 shell closure. For ground-state energies, charge radii, and neutron skins, the IMSRG(3)-N7 corrections are small, and the charge-radius differences between 52Ca, 48Ca, and 44Ca remain underpredicted. The paper also presents size-extensivity-based estimates of IMSRG(2) many-body uncertainties that are intended to be applicable beyond calcium.

Significance. If the main 2+ result holds, the paper is significant because it identifies a many-body truncation effect as the origin of a long-standing VS-IMSRG(2) discrepancy in a key closed-shell nucleus and demonstrates that the IMSRG(3)-N7 framework can quantify and reduce such uncertainties. The calculations are parameter-free with respect to the calcium observables, since the Hamiltonian is fixed from prior chiral EFT fits, and the manuscript is unusually transparent about basis and truncation convergence, including explicit statements of what is not converged. The correction to the spin-orbit charge-radius operator in Appendix B is a useful technical contribution. However, the headline 2+ correction is not converged at the largest truncation studied, so the quantitative significance of the improvement, and the closeness to EOM-CCSD(T), are not yet fully established.

major comments (2)
  1. [Sec. III A, Fig. 4, Table I] The central positive claim rests on a 0.677 MeV lowering of the 48Ca 2+ energy at emax,3b=6, E3max=18 (Table I), but the paper itself states in Sec. III A that the 2+ energy is "far from fully converged" and that "a quantitative assignment of the VS-IMSRG(3)-N7 prediction is not possible." The trend in Fig. 4 is monotonically downward with no sign of saturation at the largest truncation, so the converged correction could be substantially larger (or, less plausibly, smaller) than the reported value. As written, the abstract's claim of a "significantly better description" and the quantitative comparison with EOM-CCSD(T) and experiment go beyond what the convergence evidence supports. The authors should either provide additional truncation points or a conservative extrapolation of the remaining correction, or clearly reframe the 2+ result as a qualitative/directional improvement and adjust the abstract and conclusion accordingly.
  2. [Sec. II B, W(s -> infinity) = 0] The VS-IMSRG(3)-N7 calculation drops three-body valence-space operators before the final shell-model diagonalization, motivated by the cluster hierarchy. The authors justify this approximation by the improved consistency between IMSRG(3)-N7 and VS-IMSRG(3)-N7 results for the ground-state energy and charge radius (Figs. 2 and 3), but this consistency check is not presented for excitation energies. Since the central claim of the paper concerns the 2+ excitation energy, the effect of the discarded three-body valence-space operators on Eex(2+) is an unquantified source of error at potentially the same order as the claimed correction. A test of this approximation in a tractable system, or at least an explicit statement of its expected size for excitation energies, is needed before the magnitude of the 2+ correction can be considered established.
minor comments (5)
  1. [Abstract and Conclusion] The phrase "significantly better description of the first 2+ excitation energy of 48Ca" should be hedged to reflect the non-convergence stated in Sec. III A, e.g., "indicates a significantly better description" or "is consistent with a substantially improved description."
  2. [Table I] Table I should include a footnote that the IMSRG(3)-N7 corrections are computed at emax,3b=6, E3max=18 and that the 48Ca 2+ correction is not fully converged in the three-body model-space truncation.
  3. [Sec. III D] The general uncertainty estimates for IMSRG(2) charge radii and neutron skins are derived from corrections that are not fully converged for all observables; the text should state more explicitly that these are estimates based on truncated IMSRG(3)-N7 corrections and may be lower bounds.
  4. [Fig. 4] It would improve clarity to add a visual or textual marker on the emax,3b=6, E3max=18 point noting that this result is not converged, so that the figure cannot be misread as a final prediction.
  5. [Appendix B] The correction to the spin-orbit radius operator is clearly described, but the authors should consider adding a sentence on the numerical impact of this correction on the reported charge radii, since the manuscript otherwise focuses on small differences.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the calcium observables are genuine predictions from a fixed chiral Hamiltonian, with the 48Ca 2+ correction computed rather than fitted and convergence caveats explicitly stated.

full rationale

The derivation chain is self-contained with respect to the paper's claims. The chiral EFT Hamiltonian (1.8/2.0 EM) is fixed from prior independent fits, and the IMSRG(3)-N7/VS-IMSRG(3)-N7 calculations contain no parameters fitted to the calcium energies, radii, or skins. The central result, the lowering of the 48Ca 2+ excitation energy, is obtained by explicitly including normal-ordered three-body operators in the IMSRG flow; it is not defined in terms of the experimental value or of the IMSRG(2) result. The paper even states that the 2+ value is 'far from fully converged' and that 'a quantitative assignment ... is not possible,' so the headline claim is a directional improvement with an honest caveat, not a forced match. The W(s->infinity)=0 truncation of three-body valence-space operators is an approximation justified by the cluster hierarchy and tested by comparing IMSRG(3)-N7 and VS-IMSRG(3)-N7 ground-state energies and radii; it does not define the 2+ correction. Self-citations to prior IMSRG(3)-N7 method papers are normal method lineage, and the paper anchors its results against independent coupled-cluster benchmarks (EOM-CCSD(T), CCSDT-1). The uncertainty estimates are derived from computed IMSRG(3)-N7 corrections and size-extensivity arguments, not from fitting or from the target observables. No equation or fitted parameter reduces a predicted quantity to an input, so no circular step is present.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced, and no parameters are fitted to the calcium observables. The inputs are a chiral EFT Hamiltonian from prior fits and computational truncation choices. The load-bearing assumptions are the NO2B initial truncation, the cluster-hierarchy truncation of three-body valence-space operators, the sufficiency of the IMSRG(3)-N7 model space, and the transferability of uncertainty estimates via size extensivity.

free parameters (1)
  • Three-body model-space truncation parameters emax,3b and E3max
    Chosen by hand (emax,3b = 4, 5, 6 and E3max up to 18) to make IMSRG(3)-N7 tractable. They are convergence parameters rather than fits, but the central 2+ result is not fully converged at the largest values, so this choice directly limits the certainty of the main claim.
assumptions (4)
  • domain assumption The normal-ordered two-body (NO2B) approximation, which discards the initial residual three-body Hamiltonian W, is accurate for the soft 1.8/2.0 (EM) Hamiltonian.
    Invoked in Sec. II A when Eq. (5) replaces Eq. (4). The residual W is dropped before the IMSRG flow, and any error from this approximation is folded into the quoted many-body uncertainty.
  • domain assumption The cluster hierarchy (one-body effects dominate two-body, which dominate three-body) justifies dropping three-body valence-space operators before the final shell-model diagonalization.
    Invoked in Sec. II B for VS-IMSRG(3)-N7: W(s to infinity) is set to zero before computing valence-space interactions. This affects the 2+ spectrum claim and is not directly benchmarked against a three-body-capable solver here.
  • domain assumption The IMSRG(3)-N7 truncation captures the leading missing many-body correlations beyond IMSRG(2), so its corrections indicate IMSRG(2) uncertainty.
    The method is defined in Sec. II B and compared with CCSDT-1, but full convergence of the 2+ correction is not demonstrated, and the paper treats the uncertainty estimates as a rough rule of thumb.
  • domain assumption Size extensivity of the IMSRG allows transferring uncertainty estimates from calcium isotopes to other medium-mass systems.
    Argued in Sec. III D. The paper itself calls the transferable estimates a rough rule of thumb, not a proven bound, and notes that excitation-energy corrections are system dependent.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Improved structure of calcium isotopes from ab initio calculations." pith.science (2026). https://pith.science/paper/J3QVIUIZ

@misc{pith2026241116014,
  author       = {Pith},
  title        = {Pith review of: Improved structure of calcium isotopes from ab initio calculations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J3QVIUIZ}},
  note         = {Machine review of arXiv:2411.16014}
}
abstract

The in-medium similarity renormalization group (IMSRG) is a powerful and flexible many-body method to compute the structure of nuclei starting from nuclear forces. Recent developments have extended the IMSRG from its standard truncation at the normal-ordered two-body level, the IMSRG(2), to a precision approximation including normal-ordered three-body operators, the IMSRG(3)-$N^7$. This improvement provides a more precise solution to the many-body problem and makes it possible to quantify many-body uncertainties in IMSRG calculations. We explore the structure of $^{44,48,52}$Ca using the IMSRG(3)-$N^7$, focusing on understanding existing discrepancies of the IMSRG(2) to experimental results. We find a significantly better description of the first $2^+$ excitation energy of $^{48}$Ca, improving the description of the shell closure at $N=28$. At the same time, we find that the IMSRG(3)-$N^7$ corrections to charge radii do not resolve the systematic underprediction of the puzzling large charge radius difference between $^{52}$Ca and $^{48}$Ca. We present estimates of many-body uncertainties of IMSRG(2) calculations applicable also to other systems based on the size extensivity of the method.

Figures

Figures reproduced from arXiv: 2411.16014 by the authors.

Figure 1
Figure 1. FIG. 1. Ground-state energy (top), charge radius (mid [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The ground-state energy of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The charge radius of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The first [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of charge radii of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Low-lying excitation spectra of positive-parity states of [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Model-space convergence of [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. From bare two-nucleon interaction to nuclear matter and finite nuclei in a relativistic framework

    nucl-th 2025-07 conditional novelty 6.0 of 10

    A leading-order relativistic chiral two-nucleon force, with four constants fit to scattering data, describes nuclear matter saturation and medium-mass nuclei binding energies and radii without three-nucleon forces.

  2. Spectroscopy of $^{52}$K

    nucl-ex 2024-12 conditional novelty 6.0 of 10

    First spectroscopy of 52K reveals a 2− ground state and excited states at 293, 536, and 1076 keV, with single-particle proton configurations.

Reference graph

Works this paper leans on

87 extracted references · 35 canonical work pages · cited by 2 Pith papers

  1. [1]

    A. T. Gallant, J. C. Bale, T. Brunner, U. Chowdhury, S. Ettenauer, et al., New precision mass measurements of neutron-rich calcium and potassium isotopes and three- nucleon forces, Phys. Rev. Lett.109, 032506 (2012)

    2012

  2. [2]

    Wienholtz, D

    F. Wienholtz, D. Beck, K. Blaum, Ch. Borgmann, M. Bre- itenfeldt, et al., Masses of exotic calcium isotopes pin down nuclear forces, Nature498, 346 (2013)

    2013

  3. [3]

    Steppenbeck, S

    D. Steppenbeck, S. Takeuchi, N. Aoi, P. Doornenbal, M. Matsushita, et al., Evidence for a new nuclear ‘magic number’ from the level structure of54Ca, Nature 502, 207 (2013)

    2013

  4. [4]

    Enciu, H

    M. Enciu, H. N. Liu, A. Obertelli, P. Doornenbal, F. Nowacki, et al., Extended p3/2 neutron orbital and the N = 32 shell closure in52Ca, Phys. Rev. Lett.129, 262501 (2022)

    2022

  5. [5]

    R. F. Garcia Ruiz, M. L. Bissell, K. Blaum, A. Ekström, N. Frömmgen,et al., Unexpectedly large charge radii of neutron-rich calcium isotopes, Nat. Phys.12, 594 (2016), arXiv:1602.07906

    arXiv 2016

  6. [6]

    Koszorús, X

    Á. Koszorús, X. F. Yang, W. G. Jiang, S. J. Novario, S. W. Bai,et al., Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character ofN = 32, Nat. Phys.17, 439 (2021), arXiv:2012.01864

    arXiv 2021

  7. [7]

    H. N. Liu, A. Obertelli, D. Doornenbal, C. A. Bertulani, G. Hagen, et al. , How robust is the N = 34 subshell closure? First spectroscopy of52Ar, Phys. Rev. Lett.122, 072502 (2019), arXiv:1811.08451

    work page Pith review arXiv 2019

  8. [8]

    O. B. Tarasov, D. S. Ahn, D. Bazin, N. Fukuda, A. Gade, et al., Discovery of60Ca and implications for the stability of 70Ca, Phys. Rev. Lett.121, 022501 (2018)

    2018

Show all 87 references
  1. [9]

    M. L. Cortés, W. Rodriguez, P. Doornenbal, A. Obertelli, J. D. Holt, et al. , Shell evolution of N = 40 isotones towards 60Ca: First spectroscopy of62Ti, Phys. Lett. B 800, 135071 (2020), arXiv:1912.07887

    2020 arXiv

  2. [10]

    S. Chen, F. Browne, P. Doornenbal, J. Lee, A. Obertelli, et al., Level structures of56,58Ca cast doubt on a dou- bly magic 60Ca, Phys. Lett. B 843, 138025 (2023), arXiv:2307.07077

    2023 arXiv

  3. [11]

    W. H. Dickhoff and C. Barbieri, Self-consistent Green’s function method for nuclei and nuclear matter, Prog. Part. Nucl. Phys. 52, 377 (2004), arXiv:nucl-th/0402034

    2004 arXiv

  4. [12]

    Lee, Lattice simulations for few- and many-body systems, Prog

    D. Lee, Lattice simulations for few- and many-body systems, Prog. Part. Nucl. Phys. 63, 117 (2009), arXiv:0804.3501

    2009 arXiv

  5. [13]

    Hagen, T

    G. Hagen, T. Papenbrock, M. Hjorth-Jensen, and D. J. Dean, Coupled-cluster computations of atomic nuclei, Rep. Prog. Phys. 77, 096302 (2014), arXiv:1312.7872

    2014 arXiv

  6. [14]

    Hergert, S

    H. Hergert, S. K. Bogner, T. D. Morris, A. Schwenk, and K. Tsukiyama, The in-medium similarity renormalization group: A novel ab initio method for nuclei, Phys. Rep. 621, 165 (2016), arXiv:1512.06956

    2016 arXiv

  7. [15]

    Tichai, R

    A. Tichai, R. Roth, and T. Duguet, Many-body perturba- tion theories for finite nuclei, Front. Phys.8, 164 (2020), arXiv:2001.10433

    2020 arXiv

  8. [16]

    Hergert, A guided tour ofab initio nuclear many-body theory, Front

    H. Hergert, A guided tour ofab initio nuclear many-body theory, Front. Phys.8, 379 (2020), arXiv:2008.05061

    2020 arXiv

  9. [17]

    T.D.Morris, J.Simonis, S.R.Stroberg, C.Stumpf, G.Ha- gen, J. D. Holt, G. R. Jansen, T. Papenbrock, R. Roth, and A. Schwenk, Structure of the lightest tin isotopes, Phys. Rev. Lett.120, 152503 (2018), arXiv:1709.02786

    2018 arXiv

  10. [18]

    Miyagi, S

    T. Miyagi, S. R. Stroberg, P. Navrátil, K. Hebeler, and J. D. Holt, Convergedab initio calculations of heavy nu- clei, Phys. Rev. C105, 014302 (2022), arXiv:2104.04688

    2022 arXiv

  11. [19]

    B. S. Hu, W. G. Jiang, T. Miyagi, Z. H. Sun, A. Ekström, C. Forssén, G. Hagen, J. D. Holt, T. Papenbrock, S. R. Stroberg, and I. Vernon, Ab initio predictions link the neutron skin of 208Pb to nuclear forces, Nat. Phys.18, 1196 (2022), arXiv:2112.01125

    2022 arXiv

  12. [20]

    Hebeler, V

    K. Hebeler, V. Durant, J. Hoppe, M. Heinz, A. Schwenk, J. Simonis, and A. Tichai, Normal ordering of three- nucleon interactions forab initio calculations of heavy nu- clei, Phys. Rev. C107, 024310 (2023), arXiv:2211.16262

    2023 arXiv

  13. [21]

    Arthuis, K

    P. Arthuis, K. Hebeler, and A. Schwenk, Neutron-rich nuclei and neutron skins from chiral low-resolution inter- actions, arXiv:2401.06675

    arXiv

  14. [22]

    Hagen, M

    G. Hagen, M. Hjorth-Jensen, G. R. Jansen, R. Mach- leidt, and T. Papenbrock, Evolution of shell structure in neutron-rich calcium isotopes, Phys. Rev. Lett.109, 032502 (2012), arXiv:1204.3612

    2012 arXiv

  15. [23]

    V. Somà, A. Cipollone, C. Barbieri, P. Navrátil, and T. Duguet, Chiral two- and three-nucleon forces along medium-mass isotope chains, Phys. Rev. C89, 061301 (2014), arXiv:1312.2068

    2014 arXiv

  16. [24]

    Langhammer, and R

    H.Hergert, S.K.Bogner, T.D.Morris, S.Binder, A.Calci, J. Langhammer, and R. Roth,Ab initio multireference in-medium similarity renormalization group calculations of even calcium and nickel isotopes, Phys. Rev. C90, 041302(R) (2014), arXiv:1408.6555

    2014 arXiv

  17. [25]

    Hagen, G

    G. Hagen, G. R. Jansen, and T. Papenbrock, Structure of 78Ni from first-principles computations, Phys. Rev. Lett. 117, 172501 (2016), arXiv:1605.01477

    2016 arXiv

  18. [26]

    Hagen, A

    G. Hagen, A. Ekström, C. Forssén, G. R. Jansen, W. Nazarewicz, T. Papenbrock, K. A. Wendt, S. Bacca, N. Barnea, B. Carlsson, C. Drischler, K. Hebeler, M. Hjorth-Jensen, M. Miorelli, G. Orlandini, A. Schwenk, and J. Simonis, Neutron and weak-charge distribu- tions of the 48Ca n...

    2016 arXiv

  19. [27]

    S. R. Stroberg, A. Calci, H. Hergert, J. D. Holt, S. K. Bogner, R. Roth, and A. Schwenk, Nucleus-dependent valence-space approach to nuclear structure, Phys. Rev. Lett. 118, 032502 (2017), arXiv:1607.03229

    2017 arXiv

  20. [28]

    Simonis, S

    J. Simonis, S. R. Stroberg, K. Hebeler, J. D. Holt, and A. Schwenk, Saturation with chiral interactions and conse- quences for finite nuclei, Phys. Rev. C96, 014303 (2017), arXiv:1704.02915

    2017 arXiv

  21. [29]

    Tichai, P

    A. Tichai, P. Arthuis, T. Duguet, H. Hergert, V. Somà, and R. Roth, Bogoliubov many-body perturbation the- ory for open-shell nuclei, Phys. Lett. B786, 195 (2018), arXiv:1806.10931

    2018 arXiv

  22. [30]

    S. R. Stroberg, J. D. Holt, A. Schwenk, and J. Simonis, Ab initio limits of atomic nuclei, Phys. Rev. Lett.126, 022501 (2021), arXiv:1905.10475

    2021 arXiv

  23. [31]

    Tichai, P

    A. Tichai, P. Demol, and T. Duguet, Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory, Phys. Lett. B 851, 138571 (2024), arXiv:2307.15619

    2024 arXiv

  24. [32]

    Miyagi, S

    T. Miyagi, S. R. Stroberg, J. D. Holt, and N. Shimizu, Ab initio multishell valence-space Hamiltonians and the island of inversion, Phys. Rev. C 102, 034320 (2020), arXiv:2004.12969

    2020 arXiv

  25. [33]

    Tsukiyama, S

    K. Tsukiyama, S. K. Bogner, and A. Schwenk, In-medium 14 similarity renormalization group for nuclei, Phys. Rev. Lett. 106, 222502 (2011), arXiv:1006.3639

    2011 arXiv

  26. [34]

    Tsukiyama, S

    K. Tsukiyama, S. K. Bogner, and A. Schwenk, In-medium similarity renormalization group for open-shell nuclei, Phys. Rev. C85, 061304 (2012), arXiv:1203.2515

    2012 arXiv

  27. [35]

    S. R. Stroberg, H. Hergert, S. K. Bogner, and J. D. Holt, Nonempirical interactions for the nuclear shell model: An update, Annu. Rev. Nucl. Part. Sci.69, 307 (2019), arXiv:1902.06154

    2019 arXiv

  28. [36]

    Heinz, A

    M. Heinz, A. Tichai, J. Hoppe, K. Hebeler, and A. Schwenk, In-medium similarity renormalization group with three-body operators, Phys. Rev. C 103, 044318 (2021), arXiv:2102.11172

    2021 arXiv

  29. [37]

    S. R. Stroberg, T. D. Morris, and B. C. He, In-medium similarity renormalization group with flowing 3-body op- erators, and approximations thereof, Phys. Rev. C110, 044316 (2024), arXiv:2406.13010

    2024 arXiv

  30. [38]

    Miyagi, NuHamil: A numerical code to generate nuclear two- and three-body matrix elements from chiral effective field theory, Eur

    T. Miyagi, NuHamil: A numerical code to generate nuclear two- and three-body matrix elements from chiral effective field theory, Eur. Phys. J. A59, 150 (2023), arXiv:2302.07962

    2023 arXiv

  31. [39]

    Tichai, J

    A. Tichai, J. Müller, K. Vobig, and R. Roth, Natural orbitals for ab initio no-core shell model calculations, Phys. Rev. C99, 034321 (2019), arXiv:1809.07571

    2019 arXiv

  32. [40]

    S. J. Novario, G. Hagen, G. R. Jansen, and T. Papenbrock, Charge radii of exotic neon and magnesium isotopes, Phys. Rev. C 102, 051303(R) (2020), arXiv:2007.06684

    2020 arXiv

  33. [41]

    Hoppe, A

    J. Hoppe, A. Tichai, M. Heinz, K. Hebeler, and A. Schwenk, Natural orbitals for many-body expan- sion methods, Phys. Rev. C 103, 014321 (2021), arXiv:2009.04701

    2021 arXiv

  34. [42]

    Hagen, T

    G. Hagen, T. Papenbrock, D. J. Dean, A. Schwenk, A. Nogga, M. Włoch, and P. Piecuch, Coupled-cluster theory for three-body Hamiltonians, Phys. Rev. C76, 034302 (2007), arXiv:0704.2854

    2007 arXiv

  35. [43]

    R. Roth, S. Binder, K. Vobig, A. Calci, J. Langhammer, and P. Navrátil, Medium-mass nuclei with normal-ordered chiral N N+3N interactions, Phys. Rev. Lett.109, 052501 (2012), arXiv:1112.0287

    2012 arXiv

  36. [44]

    Binder, J

    S. Binder, J. Langhammer, A. Calci, and R. Roth,Ab initio path to heavy nuclei, Phys. Lett. B736, 119 (2014), arXiv:1312.5685

    2014 arXiv

  37. [45]

    Djärv, A

    T. Djärv, A. Ekström, C. Forssén, and G. R. Jansen, Normal-ordering approximations and transla- tional (non)invariance, Phys. Rev. C104, 024324 (2021), arXiv:2104.14820

    2021 arXiv

  38. [46]

    T. D. Morris, N. M. Parzuchowski, and S. K. Bogner, Mag- nus expansion and in-medium similarity renormalization group, Phys. Rev. C92, 034331 (2015), arXiv:1507.06725

    2015 arXiv

  39. [47]

    T. D. Morris, Systematic improvements of ab-initio in- medium similarity renormalization group calculations , Ph.D. thesis, Michigan State University (2016)

    2016

  40. [48]

    B. C. He and S. R. Stroberg, Factorized approxi- mation to the in-medium similarity renormalization group IMSRG(3), Phys. Rev. C 110, 044317 (2024), arXiv:2405.19594

    2024 arXiv

  41. [49]

    Shimizu, T

    N. Shimizu, T. Mizusaki, Y. Utsuno, and Y. Tsunoda, Thick-restart block Lanczos method for large-scale shell- model calculations, Comput. Phys. Commun.244, 372 (2019), arXiv:1902.02064

    2019 arXiv

  42. [50]

    Friman and A

    B. Friman and A. Schwenk, Three-body interactions in Fermi systems, inFrom Nuclei to Stars: Festschrift in Honor of Gerald E Brown , edited by S. Lee (2011) p. 141, arXiv:1101.4858

    2011 arXiv

  43. [51]

    S. R. Stroberg, H. Hergert, J. D. Holt, S. K. Bogner, and A. Schwenk, Ground and excited states of doubly open- shell nuclei from ab initio valence-space Hamiltonians, Phys. Rev. C93, 051301(R) (2016), arXiv:1511.02802

    2016 arXiv

  44. [52]

    A. Ong, J. C. Berengut, and V. V. Flambaum, Effect of spin-orbit nuclear charge density corrections due to the anomalous magnetic moment on halonuclei, Phys. Rev. C 82, 014320 (2010), arXiv:1006.5508

    2010 arXiv

  45. [53]

    J. L. Friar, J. Martorell, and D. W. L. Sprung, Nuclear sizes and the isotope shift, Phys. Rev. A56, 4579 (1997), arXiv:nucl-th/9707016

    1997 arXiv

  46. [54]

    R. L. Workmanet al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys.2022, 083C01 (2022)

    2022

  47. [55]

    S. R. Stroberg et al. , https://github.com/ ragnarstroberg/imsrg (2024)

    2024

  48. [56]

    Hebeler, S

    K. Hebeler, S. K. Bogner, R. J. Furnstahl, A. Nogga, and A. Schwenk, Improved nuclear matter calculations from chiral low-momentum interactions, Phys. Rev. C83, 031301(R) (2011), arXiv:1012.3381

    2011 arXiv

  49. [57]

    Noga and R

    J. Noga and R. J. Bartlett, The full CCSDT model for molecular electronic structure, J. Chem. Phys.86, 7041 (1987)

    1987

  50. [58]

    G. E. Scuseria and H. F. Schaefer, A new implementa- tion of the full CCSDT model for molecular electronic structure, Chem. Phys. Lett.152, 382 (1988)

    1988

  51. [59]

    A.G.TaubeandR.J.Bartlett,ImprovinguponCCSD(T): ΛCCSD(T). I. Potential energy surfaces, J. Chem. Phys. 128, 044110 (2008)

    2008

  52. [60]

    A.G.TaubeandR.J.Bartlett,ImprovinguponCCSD(T): ΛCCSD(T). II. Stationary formulation and derivatives, J. Chem. Phys. 128, 044111 (2008)

    2008

  53. [61]

    Binder, P

    S. Binder, P. Piecuch, A. Calci, J. Langhammer, P. Navrátil, and R. Roth, Extension of coupled-cluster theory with a noniterative treatment of connected triply excited clusters to three-body Hamiltonians, Phys. Rev. C 88, 054319 (2013), arXiv:1309.1123

    2013 arXiv

  54. [62]

    Y. S. Lee, S. A. Kucharski, and R. J. Bartlett, A coupled cluster approach with triple excitations, J. Chem. Phys. 81, 5906 (1984)

    1984

  55. [63]

    Simonis, S

    J. Simonis, S. Bacca, and G. Hagen, First principles elec- tromagnetic responses in medium-mass nuclei: Recent progress from coupled-cluster theory, Eur. Phys. J. A55, 241 (2019), arXiv:1905.02055

    2019 arXiv

  56. [64]

    Bonaiti, private communication

    F. Bonaiti, private communication

  57. [65]

    M. Wang, W. Huang, F. Kondev, G. Audi, and S. Naimi, The AME 2020 atomic mass evaluation (II). Tables, graphs and references, Chinese Phys. C45, 030003 (2021)

    2021

  58. [66]

    C. W. Johnson, W. E. Ormand, K. S. McElvain, and H. Shan, bigstick: A flexible configuration-interaction shell-model code, arXiv:1801.08432

  59. [67]

    Roth, Importance truncation for large-scale configu- ration interaction approaches, Phys

    R. Roth, Importance truncation for large-scale configu- ration interaction approaches, Phys. Rev. C79, 064324 (2009), arXiv:0903.4605

    2009 arXiv

  60. [68]

    B. R. Barrett, P. Navrátil, and J. P. Vary,Ab initio no core shell model, Prog. Part. Nucl. Phys.69, 131 (2013)

    2013

  61. [69]

    Evaluated Nuclear Structure Data File (ENSDF),https: //www.nndc.bnl.gov/ensdf/ (2024)

    2024

  62. [70]

    Taniuchi, C

    R. Taniuchi, C. Santamaria, P. Doornenbal, A. Obertelli, K. Yoneda, et al. , 78Ni revealed as a doubly magic stronghold against nuclear deformation, Nature569, 53 (2019), arXiv:1912.05978

    2019 arXiv

  63. [71]

    Tichai, S

    A. Tichai, S. Knecht, A. Kruppa, Ö. Legeza, C. P. Moca, A. Schwenk, M. A. Werner, and G. Zarand, Combining 15 the in-medium similarity renormalization group with the density matrix renormalization group: Shell structure and information entropy, Phys. Lett. B845, 138139 (2023),...

    2023 arXiv

  64. [72]

    Hoppe, C

    J. Hoppe, C. Drischler, K. Hebeler, A. Schwenk, and J. Simonis, Probing chiral interactions up to next-to-next- to-next-to-leading order in medium-mass nuclei, Phys. Rev. C 100, 024318 (2019), arXiv:1904.12611

    2019 arXiv

  65. [73]

    Caurier, K

    E. Caurier, K. Langanke, G. Martínez-Pinedo, F. Nowacki, and P. Vogel, Shell model description of isotope shifts in calcium, Phys. Lett. B522, 240 (2001), arXiv:nucl- th/0102047

    2001

  66. [74]

    Reinhard and W

    P.-G. Reinhard and W. Nazarewicz, Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional, Phys. Rev. C95, 064328 (2017), arXiv:1704.07430

    2017 arXiv

  67. [75]

    A. J. Miller, K. Minamisono, A. Klose, D. Garand, C. Ku- jawa, et al. , Proton superfluidity and charge radii in proton-rich calcium isotopes, Nat. Phys.15, 432 (2019)

    2019

  68. [76]

    Ekström, G

    A. Ekström, G. R. Jansen, K. A. Wendt, G. Hagen, T. Pa- penbrock, B. D. Carlsson, C. Forssén, M. Hjorth-Jensen, P. Navrátil, and W. Nazarewicz, Accurate nuclear radii and binding energies from a chiral interaction, Phys. Rev. C 91, 051301(R) (2015), arXiv:1502.04682

    2015 arXiv

  69. [77]

    W. G. Jiang, A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, and T. Papenbrock, Accurate bulk properties of nuclei from A = 2 to∞ from potentials with∆ isobars, Phys. Rev. C102, 054301 (2020), arXiv:2006.16774

    2020 arXiv

  70. [78]

    G. E. Brown and A. M. Green, Even parity states of16O and 17O, Nucl. Phys.75, 401 (1966)

    1966

  71. [79]

    Federman and S

    P. Federman and S. Pittel,J = 0 + states in Ca40 and Ca42, Phys. Rev.186, 1106 (1969)

    1969

  72. [80]

    Sakakura, A

    M. Sakakura, A. Arima, and J. Sebe, Shell model study of 0+ states in 40Ca, Phys. Lett. B61, 335 (1976)

    1976

  73. [81]

    Hagen and H

    G. Hagen and H. A. Nam, Computational aspects of nuclear coupled-cluster theory, Prog. Theor. Phys. Suppl. 196, 102 (2012), arXiv:1203.3765

    2012 arXiv

  74. [83]

    www.energy.gov/doe-public-access-plan

  75. [84]

    A. L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers, and Y. Xu, The effective field theory of dark matter direct detection, J. Cosmol. Astropart. Phys.2013 (02), 004, arXiv:1203.3542

    2013 arXiv

  76. [85]

    Hoferichter, J

    M. Hoferichter, J. Menéndez, and A. Schwenk, Coher- ent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses, Phys. Rev. D102, 074018 (2020), arXiv:2007.08529

    2020 arXiv

  77. [86]

    B. S. Hu, J. Padua-Argüelles, S. Leutheusser, T. Miyagi, S. R. Stroberg, and J. D. Holt,Ab initio structure factors for spin-dependent dark matter direct detection, Phys. Rev. Lett. 128, 072502 (2022), arXiv:2109.00193

    2022 arXiv

  78. [87]

    Noël and M

    F. Noël and M. Hoferichter, Uncertainty quantification for µ → e conversion in nuclei: Charge distributions, J. High Energy Phys.08, 052, arXiv:2406.06677

    arXiv

  79. [88]

    Heinz, M

    M. Heinz, M. Hoferichter, T. Miyagi, F. Noël, and A. Schwenk, Ab initio calculations of overlap integrals for µ → e conversion in nuclei, arXiv:2412.04545

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.